Universidad Complutense de Madrid
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Mazur intersection properties and differentiability of convex functions in Banach spaces

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Georgiev, P. G. y Granero, A. S. y Jiménez Sevilla, María del Mar y Moreno, José Pedro (2000) Mazur intersection properties and differentiability of convex functions in Banach spaces. Journal of the London Mathematical Society, 61 (2). pp. 531-542. ISSN 0024-6107

URL Oficial: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=53605




Resumen

It is proved that the dual of a Banach space with the Mazur intersection property is almost weak* Asplund. Analogously, the predual of a dual space with the weak* Mazur intersection property is almost Asplund. Through the use of these arguments, it is found that, in particular, almost all (in the Baire sense) equivalent norms on [script l]1(Γ) and [script l][infty infinity](Γ) are Fréchet differentiable on a dense Gδ subset. Necessary conditions for Mazur intersection properties in terms of convex sets satisfying a Krein–Milman type condition are also discussed. It is also shown that, if a Banach space has the Mazur intersection property, then every subspace of countable codimension can be equivalently renormed to satisfy this property.


Tipo de documento:Artículo
Materias:Ciencias > Matemáticas > Álgebra
Código ID:22200
Depositado:03 Jul 2013 17:31
Última Modificación:01 Feb 2016 16:11

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